LEADER 04605nam 22006975 450 001 9910917194103321 005 20250606205016.0 010 $a9781071641729$b(electronic bk.) 010 $z9781071641712 024 7 $a10.1007/978-1-0716-4172-9 035 $a(MiAaPQ)EBC31823020 035 $a(Au-PeEL)EBL31823020 035 $a(CKB)36951652000041 035 $a(DE-He213)978-1-0716-4172-9 035 $a(EXLCZ)9936951652000041 100 $a20241207d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aApplied Probability /$fby Kenneth Lange 205 $a3rd ed. 2024. 210 1$aNew York, NY :$cSpringer US :$cImprint: Springer,$d2024. 215 $a1 online resource (608 pages) 225 1 $aSpringer Texts in Statistics,$x2197-4136 311 08$aPrint version: Lange, Kenneth Applied Probability New York, NY : Springer,c2025 9781071641712 327 $aBasic Notions of Probability Theory -- Calculation of Expectations -- Convexity, Optimization, and Inequalities -- Combinatorics -- Combinatorial Optimization -- Poisson Processes -- Discrete-Time Markov Chains -- Continuous-Time Markov Chains -- Branching Processes -- Martingales -- Diffusion Processes -- Asymptotic Methods -- Numerical Methods -- Poisson Approximation -- Number Theory -- Entropy -- Appendix: Mathematical Review. 330 $aApplied Probability presents a unique blend of theory and applications, with special emphasis on mathematical modeling, computational techniques, and examples from the biological sciences. Chapter 1 reviews elementary probability and provides a brief survey of relevant results from measure theory. Chapter 2 is an extended essay on calculating expectations. Chapter 3 deals with probabilistic applications of convexity, inequalities, and optimization theory. Chapters 4 and 5 touch on combinatorics and combinatorial optimization. Chapters 6 through 11 present core material on stochastic processes. If supplemented with appropriate sections from Chapters 1 and 2, there is sufficient material for a traditional semester-long course in stochastic processes covering the basics of Poisson processes, Markov chains, branching processes, martingales, and diffusion processes. This third edition includes new topics and many worked exercises. The new chapter on entropy stresses Shannon entropy and its mathematical applications. New sections in existing chapters explain the Chinese restaurant problem, the infinite alleles model, saddlepoint approximations, and recurrence relations. The extensive list of new problems pursues topics such as random graph theory omitted in the previous editions. Computational probability receives even greater emphasis than earlier. Some of the solved problems are coding exercises, and Julia code is provided. Mathematical scientists from a variety of backgrounds will find Applied Probability appealing as a reference. This updated edition can serve as a textbook for graduate students in applied mathematics, biostatistics, computational biology, computer science, physics, and statistics. Readers should have a working knowledge of multivariate calculus, linear algebra, ordinary differential equations, and elementary probability theory. 410 0$aSpringer Texts in Statistics,$x2197-4136 606 $aStatistics 606 $aProbabilities 606 $aComputer science$xMathematics 606 $aMathematical statistics 606 $aMathematics$xData processing 606 $aEstadística matemātica$2thub 606 $aMatemātica aplicada$2thub 606 $aStatistical Theory and Methods 606 $aProbability Theory 606 $aProbability and Statistics in Computer Science 606 $aComputational Mathematics and Numerical Analysis 608 $aLlibres electrōnics$2thub 615 0$aStatistics. 615 0$aProbabilities. 615 0$aComputer science$xMathematics. 615 0$aMathematical statistics. 615 0$aMathematics$xData processing. 615 7$aEstadística matemātica 615 7$aMatemātica aplicada 615 14$aStatistical Theory and Methods. 615 24$aProbability Theory. 615 24$aProbability and Statistics in Computer Science. 615 24$aComputational Mathematics and Numerical Analysis. 676 $a519.2 700 $aLange$b Kenneth$059343 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910917194103321 996 $aApplied probability$91427051 997 $aUNINA